Question

solve for r and graph the solution. 6r - 5 ≥ 7 or -4r + 1 > -3 plot the endpoints. select an endpoint to change it from closed to open. select the middle a segment, ray, or line to delete it.

Explanation:

Step1: Isolate first inequality's $r$

Add 5 to both sides:
$6r - 5 + 5 \geq 7 + 5$
$6r \geq 12$
Divide by 6:
$\frac{6r}{6} \geq \frac{12}{6}$
$r \geq 2$

Step2: Isolate second inequality's $r$

Subtract 1 from both sides:
$-4r + 1 - 1 > -3 - 1$
$-4r > -4$
Divide by -4 (reverse inequality):
$\frac{-4r}{-4} < \frac{-4}{-4}$
$r < 1$

Answer:

The solution is $r < 1$ or $r \geq 2$.

For the graph:

• Draw an open circle at $r=1$ and a ray extending to the left (all values less than 1).
• Draw a closed circle at $r=2$ and a ray extending to the right (all values greater than or equal to 2).